Performing a Calibration Process in a Quantum Computing System

ABSTRACT

In a general aspect, calibration is performed in a quantum computing system. In some cases, domains of a quantum computing system are identified, where the domains include respective domain control subsystems and respective subsets of quantum circuit devices in a quantum processor of the quantum computing system. Sets of measurements are obtained from one of the domains and stored in memory. Device characteristics of the quantum circuit devices of the domain are obtained based on the set of measurements, and the device characteristics are stored in a memory of the control system. Quantum logic control parameters for the subset of quantum circuit devices of the domain are obtained based on the set of measurements and stored in memory.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 62/469,648 entitled “Performing a Calibration Process in a Quantum Computing System” and filed Mar. 10, 2017, which is hereby incorporated by reference.

BACKGROUND

The following description relates to performing a calibration process in a quantum computing system.

In some quantum computing architectures, qubits are implemented in superconducting circuits. The qubits can be implemented, for example, in circuit devices that include Josephson junctions. In some systems, circuit devices in a superconducting circuit are controlled by an external control module.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of an example quantum computing system.

FIG. 2 is a block diagram of an example calibration process.

FIG. 3 is a block diagram of an example calibration process.

FIG. 4 is block diagram of an example quantum computing system.

FIG. 5 is a plot of a qubit frequency versus a flux pulse.

FIG. 6 is a diagram of an example gate tune-up process.

FIG. 7 is a diagram of an example process for flux bias automation (FBA).

DETAILED DESCRIPTION

In some aspects of what is described here, a calibration process provides more efficient and accurate initialization of devices and operations in a quantum computing system.

In some implementations, a calibration process provides automated system “bring-up” for a large-scale quantum computer system. As an example, the calibration process may utilize design parameters, measured values, and automatic optimization to determine operating parameters for a multi-qubit system after installing the system in an operating environment (e.g., in a dilution refrigerator), so that the system can be efficiently accessed as working or identified as sub-optimal. In some cases, complicated characterization processes can be divided into sub-processing units that can be scaled up and applied to large systems. For instance, defining a precise calibration sequence may allow rapid characterization of specialized processors.

In some implementations, a central computer process dispatches bring-up instructions to several sub-processing units to assess a superconducting quantum circuit system. The sub-processing units can characterize the circuit devices and tune up quantum logic gates for computation. Both the characterization and the tune-up may follow a defined procedure. By subdividing bring-up tasks with a defined pass/fail criteria based on design and performance, a complex system can be brought up, characterized, and efficiently tuned-up.

FIG. 1 is a schematic diagram of an example quantum computing system 100. The example quantum computing system 100 shown in FIG. 1 includes a control system 110, a signal delivery system 106, and a quantum processor cell 102. A quantum computing system may include additional or different features, and the components of a quantum computing system may operate as described with respect to FIG. 1 or in another manner.

The example quantum computing system 100 shown in FIG. 1 can perform quantum computational tasks by executing quantum algorithms. In some implementations, the quantum computing system 100 can perform quantum computation by storing and manipulating information within individual quantum states of a composite quantum system. For example, qubits (i.e., quantum bits) can be stored in and represented by an effective two-level sub-manifold of a quantum coherent physical system. In some instances, quantum logic can be performed in a manner that allows large-scale entanglement within the quantum system. Control signals can manipulate the quantum states of individual qubits and the joint states of the multiple qubits. In some instances, information can be read out from the composite quantum system by measuring the quantum states of the individual qubits.

In some implementations, the quantum computing system 100 can operate using gate-based models for quantum computing. In some models, fault-tolerance can be achieved by applying a set of high-fidelity control and measurement operations to the qubits. For example, topological quantum error correction schemes can operate on a lattice of nearest-neighbor coupled qubits. In some instances, these and other types of quantum error correcting schemes can be adapted for a two- or three-dimensional lattice of nearest neighbor coupled qubits, for example, to achieve fault-tolerant quantum computation. Adjacent pairs of qubits in the lattice can be addressed, for example, with two-qubit logic operations that are capable of generating entanglement, independent of other pairs in the lattice.

In some implementations, the quantum computing system 100 is constructed and operated according to a scalable quantum computing architecture. For example, in some cases, the architecture can be scaled to a large number of qubits to achieve large-scale general purpose coherent quantum computing. In some instances, the architecture is adaptable and can incorporate a variety of modes for each technical component. For example, the architecture can be adapted to incorporate different types of qubit devices, coupler devices, readout devices, signaling devices, etc.

In some instances, all or part of the quantum processor cell 102 functions as a quantum processor, a quantum memory, or another type of subsystem. In some examples, the quantum processor cell includes a quantum circuit system. The quantum circuit system may include qubit devices, resonator devices and possibly other devices that are used to store and process quantum information. In some implementations, the quantum circuit system is a superconducting quantum circuit system, in which various circuit elements are capable of operating in a superconducting state. In some implementations, the quantum circuit system is an integrated quantum circuit (e.g., an integrated superconducting quantum circuit).

In some implementations, the example quantum processor cell 102 can process quantum information by applying control signals to the qubit devices or to the coupler devices housed in the quantum processor cell 102. The control signals can be configured to encode information in the qubit devices, to process the information by performing quantum logic gates or other types of operations, or to extract information from the qubit devices. In some examples, the operations can be expressed as single-qubit logic gates, two-qubit logic gates, or other types of quantum logic gates that operate on one or more qubits. A sequence of quantum logic operations can be applied to the qubits to perform a quantum algorithm. The quantum algorithm may correspond to a computational task, a quantum error correction procedure, a quantum state distillation procedure, or a combination of these and other types of operations.

FIG. 1 shows an example quantum processor cell 102A that includes a superconducting quantum circuit system 104. The example superconducting quantum circuit system 104 includes circuit devices 105 arranged in a two-dimensional device array. Eight circuit devices are shown in FIG. 1 . In some examples, some of the circuit devices 105 are qubit devices that each store a single qubit of information, and the qubits can collectively represent the computational state of a quantum processor. In some cases, the superconducting quantum circuit system 104 may include resonator devices coupled to the respective qubit devices, for instance, where each qubit device includes a superconducting quantum interference device (SQUID) loop and is capacitively coupled to a neighboring resonator device. The readout devices may be configured to generate readout signals that indicate the computational state of the quantum processor or quantum memory. In some examples, some of the circuit devices 105 are coupler devices that selectively operate on individual qubits or pairs of qubits. For example, the coupler devices may produce entanglement or other multi-qubit states over two or more qubits. The superconducting quantum circuit system 104 may include additional devices (e.g., additional qubit devices, coupler devices and other types of devices).

The example quantum circuit system 104 also includes connections 103 between neighboring pairs of the circuit devices 105. The connections 103 can provide electromagnetic communication between the connected circuit devices. In some cases, the connections 103 are implemented as capacitive or conductive connections. For instance, the connections 103 may include metal traces, capacitors and other components. The superconducting circuit devices 105 may be operated by microwave signals delivered in the quantum circuit system 104, for example, from the control system 110. Signals may be exchanged among the circuit devices 105 through the connections 103 or other signal pathways in the quantum circuit system 104.

The circuit devices 105 in the quantum circuit system 104 may be arranged in one or more regular or irregular arrays. For instance, qubit devices may be arranged in a rectilinear (e.g., rectangular or square) array that extends in two spatial dimensions (in the plane of the page), where each qubit device has four nearest-neighbor qubit devices. Qubit devices can be arranged in another type of regular or irregular array (e.g., a hexagonal array). In some instances, the array of circuit devices 204 also extends in a third spatial dimension (in/out of the page), for example, to form a cubic array or another type of regular or irregular three-dimensional array.

The example quantum processor cell 102A includes multiple domains. In FIG. 1 , a first domain 101A and a second domain 101B are shown. The quantum processor cell may include additional domains or different types of domains. Each domain includes a subset of the circuit devices 105. For instance, the first domain 101A may include a first subset of qubit devices, a first subset of coupler devices, and a first subset of readout devices, while the second domain 101A may include a second subset of qubit devices, a second subset of coupler devices, and a second subset of readout devices. Each subset may include, for example, two, five, ten or more such devices. The domains may be defined by hardware, by control logic, by connections, by software or otherwise.

In the example shown in FIG. 1 , the signal delivery system 106 provides communication between the control system 110 and the quantum processor cell 102. For example, the signal delivery system 106 can receive control signals from the control system 110 and deliver the control signals to the quantum processor cell 102. In some instances, the signal delivery system 106 performs preprocessing, signal conditioning, or other operations to the control signals before delivering them to the quantum processor cell 102.

In some instances, the signal delivery system 106 receives qubit readout signals from the quantum processor cell and delivers the qubit readout signals to the control system 110. In some instances, the signal delivery system 106 performs preprocessing, signal conditioning or other operations on the readout signals before delivering them to the control system 110. In some implementations, the signal delivery system 106 includes include input and output processing hardware, input and output connections, and other components. The input and processing hardware may include, for example, filters, attenuators, directional couplers, multiplexers, diplexers, bias components, signal channels, isolators, amplifiers, power dividers and other types of components.

In some implementations, the signal delivery system 106 and the quantum processor cell 102 are maintained in a controlled QPC environment. The QPC environment can be provided, for example, by shielding equipment, cryogenic equipment, and other types of environmental control systems. In some examples, the components in the QPC environment operate in a cryogenic temperature regime and are subject to very low electromagnetic and thermal noise. For example, magnetic shielding can be used to shield the system components from stray magnetic fields, optical shielding can be used to shield the system components from optical noise, thermal shielding and cryogenic equipment can be used to maintain the system components at controlled temperature, etc. The levels and types of noise that are tolerated or controlled in the QPC environment can vary, for example, based on the features and operational requirements of the quantum processor cell 102 and the signal delivery system 106.

In the example quantum processor unit 100 shown in FIG. 1 , the control system 110 controls operation of the quantum processor cell 102. The example control system 110 may include data processors, signal generators, interface components and other types of systems or subsystems. In some cases, the control system 110 includes one or more classical computers or classical computing components.

FIG. 1 shows an example control system 110A that includes one or more processors 112, memory 114, radio frequency (RF) or microwave (μW) generators 116, radio frequency (RF) or microwave (μW) receivers 118 and DC sources 120. A control system may include additional or different features and components. In some examples, components of the control system 110A operate in a room temperature regime, an intermediate temperature regime, or both. For example, the control system 110A can be configured to operate at much higher temperatures and be subject to much higher levels of noise than are present in the QPC environment.

In some implementations, the control system 110 includes a classical computing cluster, servers, databases, networks, or other types of classical computing equipment. For example, the memory 114 can include, for example, a random access memory (RAM), a storage device (e.g., a read-only memory (ROM) or others), a hard disk, or another type of storage medium. The memory 114 can include various forms of memory, media and memory devices, including by way of example semiconductor memory devices (e.g., EPROM, EEPROM, flash memory devices, and others), magnetic disks (e.g., internal hard disks, removable disks, and others), magneto optical disks, and CD ROM and DVD-ROM disks. The processors 112 may include one or more single- or multi-core microprocessors, one or more FPGAs or ASICs, one or more other types of data processing apparatus. The processors 112 can generate control information, for example, based on a quantum program (e.g., a quantum logic circuit, a quantum simulation, a quantum algorithm, etc.) to be performed by the quantum computing system 100 or based on other types of information.

In the example shown, the radio frequency (RF) or microwave (μW) generators 116 and the DC sources 120 can each generate control signals based on control information provided by the processors 112. The control signals can be delivered to the quantum processor cell 102 by the signal delivery system 106, for example, and interact with the circuit devices 105. In the example shown, the radio frequency (RF) or microwave (μW) receivers 118 can receive and process signals from the quantum processor cell 102. For example, receivers 118 can include a digitizer, a microwave source, and other types of signal processing components. The receivers 118 can process (e.g., digitize, or otherwise process) the signals from the quantum processor cell 102 and provide the processed information to the processors 112. The processors 112 can extract data, for example, to identify the quantum states of qubits in the quantum processor cell 102 or for other purposes.

The control system 110A may include multiple domain control subsystems. Each domain control subsystem may include a dedicated processor 112, memory 114, generator 116, receiver 118, DC source 120 and other resources. In some cases, resources are shared by multiple domain control subsystems. Each domain control subsystem in the control system 110A can control an associated domain in the quantum processor cell 102. For instance, a first domain control subsystem controls the first domain 101A and a second domain control subsystem controls the second domain 101B.

Each domain control subsystem in the example control system 110A can communicate with the devices in the associated domain in the quantum processor cell 102A. For instance, a generator 116 and DC source 120 in the first domain control subsystem can send signals to the subset of the circuit devices 105 in the first domain 101A, and a receiver 118 in the first domain control subsystem can receive signals from the subset of the circuit devices 105 in the first domain 101A; likewise, a generator 116 and DC source 120 in the second domain control subsystem can send signals to the subset of the circuit devices 105 in the second domain 101B, and a receiver 118 in the second domain control subsystem can receive signals from the subset of the circuit devices 105 in the second domain 101B.

In some instances, the control system 110 generates classical signals, including electrical waveforms or laser fields, which interact with devices in the quantum processor cell 102 to operate the quantum computing system 100; and the control system 110 may also receive classical signals back from the devices. To ensure that the classical signals are precisely tuned to the relevant device to give the desired device behavior and system operation, the control system 110 can be calibrated to the device.

In some instances, the control system 110 implements a calibration process that performs measurements on a quantum computing device and interprets those measurements to extract control parameters and device characteristics. The device characteristics can be physical attributes of the device, for example, the resonance frequency between the two lowest energy levels of a qubit. Device characteristics can be used to describe the performance of the device, for example, with respect to design goals. Control parameters can be parameters of the control system 110 that are calibrated to the device, for example, the optimal power setting for applying a read-out pulse. Correct determination of control parameters can be important, for example, to enable operation of the quantum computing system 100.

In some aspects of operation, domains of the quantum computing system 100 can be identified by operation of the control system 110. The domains can include respective domain control subsystems and respective subsets of quantum circuit devices 105 in a quantum processor 112 of the quantum computing system 100. In some instances, a first set of measurements can be obtained from a first domain 101A. The first set of measurements can be stored in a memory 114 of the control system 110. Device characteristics of the quantum circuit devices 105 of the first domain 101A can be determined by operation of the control system 110 based on the first set of measurements. The device characteristics can be stored in a memory 114 of the control system 110. The control system 110 can then determine (i.e., decide or make a determination) to obtain a second set of measurements from the first domain 101A based on the device characteristics. The determination to obtain a second set of measurements can be made automatically, for example, based on the device characteristics (and possibly other data) meeting a predefined criterion or set of criteria. For instance, the “example success criteria” described below for various experiments and measurements may be used as criteria for determining to obtain the second set of measurements. The second set of measurements can be obtained from the first domain 101A. The second set of measurements can be stored in the memory 114 of the control system 110. Quantum logic control parameters for the subset of quantum circuit devices 105 of the first domain 101A can be determined by operation of the control system 110A, based on the second set of measurements. The quantum logic control parameters can be stored in a database (e.g., a database defined in the memory 114) of the control system 110A for use in operating the first domain. An example of such a database is shown and described in connection with FIG. 4 , described below. The control system 110 may perform the same process or a similar process for the other domain 101B (e.g., in parallel or otherwise).

In some aspects of operation, the domains 101A, 101B can be defined in part by hardware, control logic, physical connections, or software in the quantum computing system 100. The quantum circuit devices 105 of the first domain can include qubit devices and readout devices. The control system 110 can include a controller (where the controller includes a cache), signal conversion circuitry, a filter, and an amplifier, as further shown and described in connection with FIG. 4 . The control system 110 can include an embedded operating system (OS) configured to communicate with the database and the controller, as further shown and described in connection with FIG. 4 . The device characteristics can include resonance frequencies and coherence times for qubit devices in the first domain. The quantum logic control parameters can include read-out pulse parameters or quantum logic gate pulse parameters for qubit devices in the first domain. For instance, the quantum logic control parameters may include the duration, power, frequency, or other parameters of a π pulse, a π/2 pulse, a two-qubit gate pulse, a readout pulse, etc. The first set of measurements or the second set of measurements can be repeated based on a success or a failure of a calibration of the first domain of the quantum computing system 100, for example, as discussed below with respect to FIG. 2 .

FIG. 2 is a block diagram of an example calibration process 200. The example calibration process 200 can determine device characteristics and control parameters in a quantum computer system. The calibration process 200 will, in general, depend on the design and architecture of the quantum computing system used. The example calibration process 200 includes a set of logical blocks, each representing an experimental measurement (e.g. M1-M3), and a procedure to determine the result of the measurement (e.g. R1-R3). The procedure specifies the measurements themselves, and a map from each measurement result to: (a) a new measurement (R1, R2); (b) a repetition of the same measurement, possibly with new parameters (e.g. R2); or (c) a terminal state, indicating success (R3) or failure of the procedure (R1-R3). On reaching the terminal state, the computer may notify one or more external systems or recipients (e.g., via email or instant message (e.g. Slack, etc.)).

As shown in FIG. 2 , the first experimental measurement M1 is obtained, and the first measurement result R1 (e.g., a device characteristic of a quantum circuit device) can be determined from the first experimental measurement M1. Based on the first measurement result R1, it can be determined to obtain a second experimental measurement M2. For instance, if a device characteristic (e.g., coherence time, qubit frequency, anharmonicity, etc.) determined from the first experimental measurement M1 meets a predefined criterion, then the process 200 may automatically determine to obtain the second experimental measurement M2; but if the device characteristic determined from the first experimental measurement M1 does not satisfy the quality criterion, the process 200 may automatically determine to move to a terminal state indicating failure F. The second experimental measurement M2 can then be obtained, and the second measurement result R2 (e.g., quantum logic control parameters for a quantum circuit device) can be determined from the second experimental measurement M2. For instance, if a quantum logic parameter determined from the second experimental measurement M2 meets a predefined criterion, then the process 200 may automatically determine to obtain the third experimental measurement M3; but otherwise, the process 200 may automatically determine to move to a terminal state indicating failure F, or to repeat the second experimental measurement M2 (e.g., using different parameters, etc.). The process 200 can continue in a similar, automated manner for one or more further experimental measurements (e.g., the third experimental measurement M3) and one or more further measurement result determinations (e.g., measurement result R3) until reaching a state representing success S or failure F. The predefined criteria used at R1, R2, R3 can include the “example success criteria” described below or other types of criteria.

The example calibration process 200 is modular in that it may include several sub-procedures. A modular sub-procedure may be reused to implement a characterization or calibration procedure for different kinds of devices that share a common component. When the sub-procedure terminates it returns control to the main procedure which uses the result to determine what to do next. The modular sub-procedures may also be used independently of the full experimental procedure. For example, a certain set of control parameters optimal values may drift over time and a sub-procedure to re-calibrate just those parameters that have drifted need not require a full run of the experimental procedure. This enables on-line calibration, where the operation of the device does not need to be completely paused in order to recalibrate.

In some cases, there are constraints on measurement ordering, as some measurements may only give useful results if particular control parameters or device characteristics are known to sufficient precision. The experimental procedure can take this into account, for instance, by only allowing such measurements downstream from the measurement(s) that determine the parameters or characteristics required. Each measurement can determine one or more device characteristics or control parameters (possibly to finite precision). At the end of each measurement, the measured characteristics or parameters can be committed to the memory. Thus, as the procedure progresses and eventually terminates, a store of the characteristics and parameters is constructed. In some implementations, all the characteristics and parameters of interest can be measured and stored.

In some instances, to determine the result of a measurement, the logical measurement block includes a procedure that takes as an input the measurement data and outputs: (a) extracted values for the characteristics and parameters, and (b) a member of the discrete set of outputs used to select the next measurement. In (b), the possibility that the measurement failed to produce meaningful results can be accounted for. If the problem is recoverable, like an insufficient scan range, or additional averaging is necessary, the measurement may be repeated with new parameters. If the error is not recoverable, the experimental procedure may exit to a failure state. Techniques for determining whether the measurement has succeeded or failed may be statistical in nature, based on some goodness of fit metric for fitted data (e.g. reduced residual chi-squared statistic, Akaike Information Criterion, Bayesian Information Criterion, etc.), based on machine learning, or some combination thereof.

FIG. 3 is a block diagram of an example calibration process 300. The example calibration process can be performed in a quantum computing system, for example, to characterize and tune up components of the quantum computing system. For instance, the example calibration process 300 may be used to calibrate one or more domains, subsystems or devices in the example quantum computing system 100 shown in FIG. 1 . In some cases, the calibration process 300 is controlled by a control system of the quantum computing system. The process 300 may include additional or different operations, and the operations may be performed in the order shown or in another order. In some cases, multiple operations are combined, performed in parallel or divided into additional operations.

In some cases, multiple instances of the process 300 are applied in parallel in the respective domains of a quantum computing system. In some cases, portions of the process 300 may be iterated periodically during operation of the quantum computer system.

At 302, a continuous wave (CW) initialization process is performed. The CW initialization process may include one or more of the operations described in the “1. CW Bring-up” section below. In the examples described, CW measurements are performed over time scales that are significantly longer than the coherent lifetimes of the qubits. At 304, a pulsed initialization process is performed. The pulsed initialization process may include one or more of the operations described in the “2. Pulse Bring-up” section below. In the examples described, pulsed measurements are performed over time scales that are shorter than the coherent lifetimes of the qubits.

At 306, a single-qubit gate initialization process is performed. The single-qubit gate initialization process may include one or more of the operations described in the “3. Gate Tune-up” section below. At 308, a multi-qubit gate initialization process is performed. The multi-qubit gate initialization process may include one or more of the operations described in the “5. Multi-qubit Gate Tune-Up” section below.

At 310, the quantum computer system is operated. For example, the quantum computer system may execute quantum logic circuits or other types of quantum algorithms. At 312, one or more of the domains, subsystems or devices in the quantum computing system is recalibrated. The recalibration may include one or more iterations of the operations (302, 304, 306, 308) applied to the whole quantum computing system or to a specific domain, subsystem or device in the quantum computing system.

FIG. 4 is a block diagram of an example quantum computing system 400. In some cases, the features and components shown in FIG. 4 may be used to implement aspects of the example quantum computing system 100 shown in FIG. 1 . In various implementations, an embedded operating system (OS) 401 serves as a central controller of the system. The embedded operating system 401 may be a real-time operating system embedded on a chip, for example, a field-programmable gate array (FPGA). The embedded operating system 401 may be a kernel (for example, a Linux kernel) embedded on a chip (for example, the FPGA). The embedded operating system 401 may run on a physical CPU with a low-latency connection to the rest of the hardware system of quantum computing system.

In some implementations, the embedded operating system 401 can communicate with various databases, the databases comprising larger-latency memory caches. The databases can include a predictions database 402, a data model database 403, and a constraints database 404. In another implementation, while three separate databases are shown in diagram 400, the databases may be consolidated into one database. The databases can contain information pertaining to quantum system and device predictions (for example, via the predictions database 402), the models for extracting parameters from the data (for example, via the data model database 403), and the constraints for determining success criteria for the calibration steps (for example, via the constraints database 404). The data associated with the databases may be stored, for instance, on a centralized server. The centralized server can be available for asynchronous updates. The data may also be stored on-board, for example, on an FPGA controller. This can allow for low-latency access which may be needed for a given operation of the quantum system.

In some implementations, the operating system can execute a multitude of processes to calibrate the QPU system, as described variously herein. The processes may be executed in parallel. Each process (for example, process 0 405, process 1 415, and process N, not shown) may utilize a stack for operation. Examples of such stacks shown in FIG. 4 include stack 0 406, stack 1 416, or stack N 426, where N is a positive integer. In some implementations, the stacks, for example, stack 0 406 and stack 1 416, can include electronics, for example, the electronics labeled as controller 0 407 and controller 1 217 in FIG. 4 . Controller 0 407 can include a cache M0 408, a digital-to-analog converter (DAC), and an analog-to-digital converter (ADC) shown as DAC/ADC 0 410 in FIG. 4 , a signal chain comprising a filter and an amplifier shown as FILTER/AMP 0 412 in FIG. 4 , and relevant QPU elements, shown as QPU ELEM 0 414 in FIG. 4 . Similarly, the controller 1 417 can include a cache M1 418, a DAC and an ADC shown as DAC/ADC 1 420, a signal chain comprising a filter and an amplifier shown as FILTER/AMP 1 422 in FIG. 4 , and relevant QPU elements, shown as QPU ELEM 1 424 in FIG. 4 . Similar components can be defined for additional controllers N (not shown), which can be part of a stack N 426. In some implementations, the QPU elements (for example, QPU ELEM 0 414 and QPU ELEM 1 424) may include couplings to other parts of the QPU which may be relevant to the execution of particular operations.

In the following text, a detailed list of example experiments is described. Each experiment provides an example of the equipment and operations to perform all or part of an initialization or calibration process. A central server or other processor can dispatch the processes to sub-processing units or domain control subsystems that operate a domain in a quantum processor cell. In each experiment, the qubits and their measured properties, whose design parameters have been journaled, may be compared and evaluated. The step-by-step process coupled with the computing architecture may allow for the tune-up of large scale superconducting quantum circuit systems.

-   -   1. Continuous wave (CW) bring-up         -   a. CW cavity spectroscopy             -   i. Instruments can include RF signal generator with                 amplitude and frequency control, RF signal receiver.             -   ii. Single tone continuous-wave measurement                 -   1. A two-dimensional power and frequency scan is                     performed on the resonator drive line. RF reflected                     off the resonator is measured. Both the power and                     the phase of the reflected field are measured at                     each point. Reflection amplitude dips and resonant                     phase rolls are noted as likely resonators.                     Cross-correlation with designed resonator frequency                     allows identification of likely resonators.                 -   2. Nonlinear response from the resonator, known as                     the Lamb shift, denotes the presence of a nonlinear                     system interacting with the resonator. Cavity                     responses taken at a higher power above the                     nonlinear response are referred to as the high-power                     branch. Cavity responses taken at a lower power                     below the nonlinear response are referred to as the                     low-power branch. The measurement system decides                     whether a successful qubit is addressable via this                     drive line with the existence of this lamb shift.             -   iii. Example success criteria can include: (A) Fitted                 resonator Q and fitted resonant frequency are compared                 to design Q and frequency, a conformance window is                 specified to denote success. (B) Measured Lamb shift                 versus predicted Lamb shift is also compared to design                 intent, a conformance window is specified to denote                 success. Criteria (A) and (B) may both need to be                 satisfied.         -   b. CW qubit spectroscopy             -   i. Instruments can include: 2× RF signal generator with                 amplitude and frequency control, and a RF signal                 receiver             -   ii. Two-tone continuous wave measurement                 -   1. A single tone on the low power branch of a                     resonator-qubit system is reflected off the                     resonator. The reflected signal is constantly                     monitored for both its reflected power and its                     reflected phase. A second tone is swept in both                     frequency and power along a qubit drive line. The                     response of the first tone reflecting off the cavity                     will exhibit changes in its reflected behavior.                     These changes will occur when systems coupled to the                     cavity change the cavity dressed state as they are                     resonantly driven. Cross correlating spectrum of the                     designed qubit with observed transition frequencies                     and transition strengths for constant drive power,                     the system assigns energy level transition                     frequencies of single or multi-photon transitions in                     the qubit.             -   iii. CW Qubit T1 and T2 estimation                 -   1. Automatic operation: After identification of the                     single photon transition from the 0 qubit state to                     the 1 qubit state, a variation of the above                     experiment is performed. Iteratively lowering the                     qubit drive power and the resonator probe power, the                     Lorentzian response of the qubit is probed at lower                     and lower powers. The system fits Lorentzian to the                     qubit until the signal to noise reaches a specific                     cutoff. The lowest achievable linewidth of the qubit                     acts as an indication of the incoherent linewidth of                     the qubit, indicating the approximate T1 relaxation                     time. The measurement system can determine to mark                     the qubit as viable for computation if the T1 is                     larger than a preset number.                 -   2. Semi-Automatic operation: After identification of                     the single photon transition from the 0 qubit state                     to the 1 qubit state, a variation of the above                     experiment is performed. An algorithm iteratively                     suggests lowering the qubit drive power and the                     resonator probe power. Each suggestion can be easily                     manipulated by the operator, or the operator can                     accept the algorithm's suggested experimental                     parameters. A measurement is run with the new                     experimental parameters. The system fits Lorentzian                     to the qubit until the signal to noise reaches a                     specific cutoff. The lowest achievable linewidth of                     the qubit acts as an indication of the incoherent                     linewidth of the qubit, indicating the approximate                     T1 relaxation time. The measurement system can                     determine to mark the qubit as viable for                     computation if the T1 is larger than a preset                     number.             -   iv. Example success criteria can include: (A) Fitted                 transition frequencies for the 0 to 1 energy splitting                 and the 0-2 energy splitting are compared to design                 intent within a conformance window. (B) Qubit linewidth                 is compared to a minimum achievable linewidth metric,                 achieving a linewidth less than the minimum passable                 linewidth denotes a success. Criteria (A) and (B) may                 both need to be satisfied.         -   c. CW Josephson parametric amplifier (JPA) single-tone             spectroscopy             -   i. Instruments can include: RF signal generator with                 amplitude and frequency control, RF signal receiver,                 controllable constant current source to set magnetic                 flux through SQUID loop.             -   ii. Single tone continuous wave measurement                 -   1. The Josephson parametric amplifier circuit is a                     single port device constructed of a low Q resonator                     with a tunable SQUID. RF is sent into the JPA with                     the use of a microwave circulator. A tunable                     resonant mode with a flux dependent resonant                     frequency is observed in a 2D plot of applied flux                     versus tone frequency. The reflected RF phase (and                     to a lesser extent the amplitude) provides a means                     of distinguishing the resonant frequency of the                     tunable mode. Due to the asymmetry in the Josephson                     Junctions a large modulation of frequencies should                     be accessible, observing a repetitive pattern                     indicates a well behaved JPA.             -   iii. Example success criteria can include: (A) A                 successful fit, with low chi squared, to the periodic                 modulation of the resonant frequency denotes success.         -   d. CW JPA gain optimization             -   i. Instruments can include: a 2× RF signal generator                 with amplitude and frequency control, RF signal                 receiver, tunable constant current source to set                 magnetic flux through SQUID loop.             -   ii. Two-tone continuous wave measurement                 -   1. Both a pump RF tone and a signal tone are sent                     into the JPA via a microwave circulator. Using a                     directed search algorithm, the pump tone's frequency                     and power are scanned by the automated search                     algorithm along with the applied flux to the JPA.                     The signal tone's frequency is chosen to be the                     frequency we are interested in amplifying. The                     signal tone is measured both with and without the                     pump tone present multiple times. Amplification and                     noise in the repeated measurements are measured. The                     amplification divided by the noise in the                     amplification are sent to the directed search                     algorithm to maximize their ratio for a given pump                     frequency, power and applied flux.             -   iii. Example Success Criteria can include: (A) The                 amount of gain achieved is compared to the design                 specification for minimum gain, success denotes                 measuring more gain than the minimum required.     -   2. Pulse bring-up         -   a. Cavity spectroscopy             -   i. Instruments can include: pulsed RF signal generator                 with amplitude and frequency control, Pulsed RF signal                 receiver             -   ii. 2D cavity spectroscopy                 -   1. A measurement is performed with pulses longer                     than the cavity ring-up time. Varying the power of                     the RF pulse and the frequency of the pulse a two                     dimensional scan is taken. Fitting the reflected                     power or frequency response of the demodulated                     reflected pulses a lamb shift measurement is                     observed. Pattern recognition algorithms discover                     the low power branch and identify possible pulse                     parameters to save as a candidate readout point,                     including the frequency and power of the pulse for                     an on-resonant low power interrogation of the                     readout resonator.             -   iii. Example success criteria can include: (A)                 Successful 1D fits of cavity response versus frequency                 denote success. (B) Producing a candidate readout point                 also denotes success. Criteria (A) and (B) may both need                 to be satisfied.         -   b. Rabi spectroscopy of the qubit             -   i. Instruments can include: 2× pulsed RF signal                 generator with amplitude and frequency control, and a                 pulsed RF signal receiver.             -   ii. Pulsed measurement involving a qubit drive pulse and                 a cavity interrogation                 -   1. Using the frequency discovered by 1.b.iii. CW                     Qubit T1/T2 estimation, qubit pulses much shorter                     than the coherent lifetime of the qubit are sent at                     varying frequencies to the qubit drive line.                     Subsequent interrogation of the cavity is recorded                     for each pulse that is sent. The response of the                     cavity resonator will trace out a coherent Rabi line                     shape of the qubit.                 -   2. Or Using the frequency discovered by 1.b.iii. CW                     Qubit T1/T2 estimation, qubit pulses much longer                     than the coherent lifetime of the qubit are sent to                     the qubit drive line. Subsequent interrogation of                     the cavity is recorded for each pulse that is sent.                     The response of the cavity resonator will trace out                     an incoherent Lorentzian at the qubit frequency.             -   iii. Example success criteria can include: (A)                 Successful fit to qubit resonance, either a driven Rabi                 lineshape (1) or a Lorentzian lineshape (2) can denote                 success.         -   c. Power Rabi             -   i. Instruments can include 2× pulsed RF signal generator                 with amplitude and frequency control, and pulsed RF                 signal receiver             -   ii. Pulsed measurement involving a qubit drive pulse and                 a cavity interrogation                 -   1. Given a successful frequency measurement and                     response from measurement 2.b. A fixed-time interval                     pulse is sent to the qubit drive line. Followed by a                     subsequent cavity interrogation. The amount of RF                     power is varied from 0 to a maximum achievable from                     the RF instrumentation. At each RF power the                     cavity's response will mirror the state of the                     qubit. Oscillations are fit to a simple                     power-broadened Rabi flopping model, where a                     sinusoid with qubit-drive, amplitude-dependent                     frequency is observed.                 -    a. Advanced readout calibration is also                     accomplished by defining the axis in I/Q space with                     the largest variance from the measurement. This                     defines the optimal quadrature. All subsequent                     measurements can be projected onto the saved optimal                     quadrature.             -   iii. Success criteria can include: (A) Successful fit to                 a power Rabi curve denotes success. (B) Amplitude to                 Rabi Frequency conversion is compared to design intent,                 agreement to conformance window denotes success.                 Criteria (A) and (B) may both need to be satisfied.         -   d. Ramsey spectroscopy             -   i. Instruments can include: 2× pulsed RF signal                 generator with amplitude and frequency control, and                 pulsed RF signal receiver             -   ii. Pulsed measurement involving two separated qubit                 drive pulses and a cavity interrogation                 -   1. A π/2 pulse is sent down the qubit drive line,                     after a variable duration of no RF pulse another π/2                     pulse is sent down the qubit drive line, followed by                     a cavity interrogation pulse. By varying the delay                     time and plotting the cavity response as a function                     of delay time a Ramsey spectrum can be observed.                 -    a. Additionally, the second π pulse can be given a                     phase offset. This phase offset mimics the local                     oscillator of the qubit drive as having been detuned                     during the variable duration wait time. Subsequently                     the Ramsey spectrum will have a clear frequency                     offset which allows for easier data fitting between                     the timescales of the Ramsey oscillation and the                     decay of the coherence of the qubit.                 -    b. Both measurements allow for carefully fitting                     the qubit resonance.             -   iii. Example Success Criteria can include: (A)                 Successful fit to a Ramsey curve denotes success. (B)                 Detuning fit parameter must not exceed expected detuning                 parameter beyond a conformance window. Criteria (A)                 and (B) may both need to be satisfied.         -   e. Power Rabi             -   i. Measurement 2.c.i. Is repeated with the newer more                 accurate qubit frequency/detuning.             -   ii. Example success criteria can include: (A) Successful                 fit to a Power Rabi curve denotes success. (B) Amplitude                 to Rabi Frequency conversion is compared to design                 intent, agreement to conformance window denotes success.                 Criteria (A) and (B) may both need to be satisfied.         -   f. T1             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude and frequency control, and                 pulsed RF signal receiver.             -   ii. Pulsed measurement involving one qubit drive pulse,                 a variable delay, and a cavity interrogation.                 -   1. Using the pulse parameters from 2.d. and 2.e. The                     state of the qubit is inverted via a π pulse. A                     variable delay where no RF is performed on the qubit                     of interest. After each delay a cavity interrogation                     tone is sent to probe the cavity's response and map                     the state of the qubit. Repeating the experiment                     many times the relaxation time to the qubit ground                     state is measured.                 -    a. Delay times are made from logarithmically spaced                     samples to probe very large ranges of possible delay                     times.             -   iii. Example Success Criteria can include: (A)                 successful fit to a decay curve denotes success. (B) The                 decay constant must be sampled at a sufficiently long                 timescale, measurements are repeated increasing the                 sampling time in a fixed manner until the sampling time                 and the decay constant meet an explicit ratio to within                 a conformance window. Criteria (A) and (B) may both need                 to be satisfied.         -   g. T2 taken with Ramsey Spectroscopy             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 and a pulsed RF signal receiver.             -   ii. Pulsed measurement involving two separated qubit                 drive pulses and a cavity interrogation                 -   1. A π/2 pulse is sent down the qubit drive line,                     after a variable duration of no RF pulse another π/2                     pulse is sent down the qubit drive line, followed by                     a cavity interrogation pulse. By varying the delay                     time and plotting the cavity response as a function                     of delay time a Ramsey spectrum can be observed.                 -    a. Additionally, the second π pulse can be given a                     phase offset. This phase offset mimics the local                     oscillator of the qubit drive as having been detuned                     during the variable duration wait time. Subsequently                     the Ramsey spectrum will have a clear frequency                     offset which allows for easier data fitting between                     the timescales of the Ramsey oscillation and the                     decay of the coherence of the qubit. Performing the                     measurement such that the frequency offset                     oscillations and the T2* act on sufficiently                     separated (>5×) timescales allows for good fitting                     of the data and accurate extraction of the T2* time.             -   iii. Example success criteria can include: (A)                 Successful fit to a Ramsey curve denotes success. (B)                 The Ramsey curve decay constant must be sampled at a                 sufficiently long timescale, measurements are repeated                 increasing the sampling time in a fixed manner until the                 sampling time and the decay constant meet an explicit                 ratio to within a conformance window. Criteria (A)                 and (B) may both need to be satisfied.     -   3. Gate tune-up         -   a. Readout optimization             -   i. Instruments can include a 2× Pulsed RF signal                 generator with amplitude and frequency control, and a                 pulsed RF signal receiver.             -   ii. Pulsed measurement to optimize the readout fidelity                 -   1. For subsequent measurements cavity interrogation                     parameters need to be more precisely set. Repeatedly                     inverting the qubit population via a π pulse on the                     qubit drive line followed by a cavity interrogation                     supplies a histogram of cavity responses. Performing                     the same measurement without the qubit inversion                     provides cavity responses for the qubit in the                     ground state. Training a binary classifier on the                     separation of these two data sets with normal ROC                     curve metrics provides objective functions that can                     be optimized by changing the cavity interrogation                     parameters. Feeding these objectives into an                     automatic system that repeats the measurements to                     maximize the achievable assignment fidelity by                     optimizing the cavity interrogation time, frequency,                     and power allows the system to tune itself to                     optimal readout conditions.                 -    a. Optimal quadrature settings are updated with the                     further refined cavity interrogation parameters.             -   iii. Example Success Criteria can include: (A) Measured                 readout fidelity may need to meet or exceed design                 specification.         -   b. AC Stark coefficient measurement             -   i. Instruments can include: 2× pulsed RF signal                 generator with amplitude, frequency, and phase control,                 pulsed RF signal receiver             -   ii. Pulsed measurement to optimize drive detuning                 -   1. Qubit driving fields are detuned from multiple                     different transitions. Detuned driving of these                     resonances causes dispersive shifts on these levels                     leading to a power dependent shift of the ground to                     first excited state of the qubit. Scanning the                     amplitude of a power dependent tuning coefficient                     repeated pulse sequences bringing the qubit                     partially toward its excited state and then back to                     the ground state are sent to the qubit along the                     qubit drive line followed by a cavity interrogation.                     For longer and longer sequences of repeated pulses                     the error associated with detuning can be amplified.                     The AC stark coefficient is found to be optimal when                     the qubit returns to its ground state. This value is                     saved, and subsequent pulses are modulated by this                     coefficient.             -   iii. Example success criteria can include (A) Measured                 AC stark coefficient must conform to design window                 specifications. (B) Fidelity of returning to ground                 state may need to be greater than predefined success                 criteria. Criteria (A) and (B) may both need to be                 satisfied.         -   c. π-π Amplitude tune-up             -   i. Instruments can include: a 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 Pulsed RF signal receiver.             -   ii. Pulsed measurement to optimize over and under                 rotation errors                 -   1. To optimize the effect of gates on the qubit,                     repeated applications of the same gate are performed                     on the qubit. Errors in the parameters of the gate                     will cause over (or under) rotation of the qubit                     state. By performing sequences that should nominally                     return the qubit to its initial state, any deviation                     from idealized pulses will cause there to be a                     different qubit state measured.                 -    a. The qubit is first rotated by a π/2 pulse to be                     in a superposition of the ground and excited state,                     placing the state of the qubit on or near the                     equator of the Bloch sphere. An even number of                     subsequent π/2 pulses (0, 2, 4, 6, etc.) are then                     sent to the qubit. For an optimal pulse this will                     rotate the qubit to the equator again. Subsequent                     cavity interrogations will reflect the state of the                     qubit. Any deviation of the qubit state (as measured                     by the cavity) from its original position on the                     Bloch sphere will be indicative of an under or over                     rotation. An optimization algorithm automatically                     adjusts the amplitude of the pulse to correct for                     over/under rotation errors by probing larger numbers                     of applied pulses, such that small errors are                     amplified.                 -    b. The qubit is first rotated by a π/2 pulse to be                     in a superposition of the ground and excited state,                     placing the state of the qubit on or near the                     equator of the Bloch sphere. Any number of                     subsequent n pulses (0, 1, 2, 3, etc.) are then sent                     to the qubit. For an optimal pulse this will rotate                     the qubit to the equator again. Subsequent cavity                     interrogations will reflect the state of the qubit.                     Any deviation of the qubit state (as measured by the                     cavity) from its original position on the Bloch                     sphere will be indicative of an under or over                     rotation. An optimization algorithm automatically                     adjusts the amplitude of the pulse to correct for                     over/under rotation errors by probing larger numbers                     of applied pulses, such that small errors are                     amplified.             -   iii. Example success criteria can include: (A) A                 fractional deviation from the equator is calculated and                 an inferred over/under rotation error is calculated,                 this is compared to a passing criterion associated with                 the number of pulses performed.         -   d. DRAG tune-up             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 and Pulsed RF signal receiver.             -   ii. Pulsed measurement to optimize leakage error from                 driving the qubit to its second excited state.                 -   1. So-called leakage errors occur when                     power-broadening of the qubit linewidth starts to                     show significant coherent drive to the second                     excited state of the qubit. Reducing this can be                     accomplished by applying a derivative of the pulse                     envelope to the opposite RF driving quadrature. The                     amplitude of this opposite quadrature drive signal                     can be scaled by a unitless coefficient. Optimally                     setting this coefficient to maximally reduce leakage                     will reduce gate infidelity. Different sequences of                     pulses that are especially sensitive to detuning                     errors when driving the qubit, like mixtures of π/2                     pulses about X and π/2 pulses about Y will exhibit                     opposite signed errors. By playing repeated                     sequences of X/2 and Y/2 pulses the error can be                     amplified. Sending repeated X/2, Y/2 sequences along                     the qubit drive line followed by a cavity                     interrogation pulse allows us to map the position of                     the qubit on the Bloch sphere. Repeating the                     experiment but permuting the order of the π/2 pulses                     (to Y/2, X/2) can cause residual error to accumulate                     in the opposite direction along the Bloch sphere.                     The difference between these two signals is fed into                     an optimizer that changes the DRAG amplitude                     coefficient. The optimizer works to minimize the                     difference between these two measurements and saves                     the DRAG amplitude coefficient such that all pulses                     know include the DRAG correction.             -   iii. Example success criteria can include: (A) The                 goodness of fit for the fitted crossing of the two                 measurements is compared to a minimum goodness of                 fit. (B) The fitted DRAG coefficient must fall within a                 specified window to denote success. Criteria (A) and (B)                 may both need to be satisfied.         -   e. π-π Fine-tune             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 and a pulsed RF signal receiver.             -   ii. Pulsed measurement to optimize over and under                 rotation errors                 -   1. A repetition of measurement 3.c is performed                     after the inclusion of DRAG.             -   iii. Example success criteria can include: (A) A                 fractional deviation from the equator is calculated and                 an inferred over/under rotation error is calculated,                 this is compared to a passing criterion associated with                 the number of pulses performed.         -   f. Perform randomized benchmarking             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 and a Pulsed RF signal receiver             -   ii. Pulsed measurement to verify functionality of tuned                 gates                 -   1. For a given circuit length a random quantum                     circuit is constructed by choosing elements from the                     Clifford algebra group, including the last elements                     which effectively invert the operation of all                     previous elements on the qubit. This procedure is                     repeated multiple times. For each random circuit the                     pulses are sent to the qubit followed by a cavity                     interrogation and the result is saved. Gate errors                     and state preparation and measurement errors will                     lead to the qubit not being measured in the ground                     state. This experiment is repeated for multiple                     random circuits and for multiple lengths of random                     circuits. Gate fidelity is inferred by fitting the                     averaged results of all these measurements by a                     power-law function as at low fidelities or at long                     times the constant application of gates will drive                     the qubit to the equator of the Bloch sphere.             -   iii. Example success criteria can include: (A) A minimum                 achieved gate fidelity must be fit to denote success.         -   g. Perform further benchmarking algorithms             -   i. Instruments can include: 2× Pulsed RF signal                 generator with amplitude, frequency, and phase control,                 and a pulsed RF signal receiver             -   ii. Perform Gate Set Tomography                 -   1. To verify the gate unitaries and the measurement                     accuracy Gate Set Tomography is performed.             -   iii. Example success criteria can include: (A) A minimum                 achieved gate fidelity must be fit to denote success.     -   4. Tunable qubit bring-up (automated bring-up variation for         flux-tunable qubits)         -   a. Instruments can include: a 2× Pulsed RF signal generator             with amplitude, frequency, and phase control, Pulsed RF             signal receiver, tunable constant current source to set             magnetic flux through SQUID loop.         -   b. In a loop over flux bias values bring up qubit similar             to (2) above: Before beginning a loop of bring-ups for             different flux settings, follow the normal bring-up             procedure (2) for a starting flux value.         -   Strategy I: Terminate after 1 flux period, adjust step size             to achieve fixed delta in qubit frequency.         -   Strategy II: Specify a sequence of flux bias values.         -   Following either strategy I or II.             -   i. Set constant current source to new constant flux bias                 current, changing it at a controlled rate.             -   ii. Choose readout settings                 -   1. For dispersive readout, perform measurement                     2.a.i., set readout frequency to be on resonance                     with cavity resonance.                 -   2. For high-power (nonlinear) readout, use                     previously saved readout settings.             -   iii. Perform qubit spectroscopy as specified in (2.c)                 and project IQ data onto most recently measured optimal                 readout axis.             -   iv. Perform power Rabi measurement as in 2.c.             -   v. Optimize readout as in (3.a) and update the readout                 settings (frequency, power, pulse width, or any set of                 parameters of the readout pulse and readout acquisition                 system).             -   vi. Measure T1 as in 2.f.                 -   1. Guess the T1 value to be measured.                 -    a. In the first iteration of the loop this is                     brought in from a previous instance of (2.f) at a                     nearby (or the same) flux bias.                 -    b. For subsequent guesses, extrapolate from                     previous guesses.                 -    i. Due to noise (including non-Markovian noise) in                     the T1 measurements, digital filtering is employed                     to smooth the data.                 -    1. Exponentially weighted averaging to extrapolate                     future iterations is employed.             -   vii. Measure T2* as in 2.g. (Ramsey)                 -   1. Guess the T2 value to be measured.                 -    a. We follow the same strategy as in (4.b.vi.1),                     for the same reasons (noise in T2* values).             -   viii. Measure T2 and CPMG                 -   1. Pulsed measurement for extracting T2 and noise                     sensitivity of qubit.                 -    a. Performing a Ramsey T2* experiment as in 2.g but                     with the inclusion of π (echo) pulses the qubit's                     response to different numbers of echo pulses can be                     mapped out. Measurements are performed where the                     delay time is evenly divided by the number of echo                     pulses performed on the qubit.         -   c. Fit the qubit frequency versus flux bias data to a model             and extract Hamiltonian parameters with uncertainties.         -   d. Generate the pure dephasing rate (1/T2-1/2T1) and the             gradient of the transition frequency f01 and fit the data to             a linear equation and extract the flux noise amplitude and             the background noise level.         -   e. At a flux insensitive point (f_(min) or f_(max)):             -   i. Perform gate tune-up as in (3) above.             -   ii. Perform benchmarking as in (3.g.) above.     -   5. Multi-qubit gate tune-up         -   a. Instruments can include 4× Pulsed RF signal generator             with amplitude, frequency, and phase control, 2× Pulsed RF             signal receiver         -   b. Measure qubit-qubit coupling             -   i. Fixed coupling designs                 -   1. π—Ramsey measurement                 -    a. After both qubits have been individually tuned                     for Single qubit operation a variation on the Ramsey                     experiment (2.d) is performed. On one qubit,                     designated as qubit A, a Ramsey experiment (2.d.) is                     performed. Immediately preceding this measurement on                     the other qubit, designated as qubit B, a π pulse is                     sent exciting qubit B to its first excited state. A                     Ramsey curve is fit to qubit A's resonator response.                     The difference between the fitted detuning and the                     expected detuning is denoted as the qubit A—qubit B                     chi.                 -   2. Example success criteria can include: (A) The                     fitted chi is compared to the designed chi.             -   ii. Tunable qubit designs                 -   1. For weak coupling, π-Ramsey measurement                 -    a. At a given constant current flux bias                     measurement 5.b.i.1.a is performed.                 -    2. For strong coupling, avoided crossing Rabi                     spectroscopy                 -    a. A tunable qubit, designated qubit A, is tuned                     into resonance with another qubit, designated                     qubit B. Similar to 2.b, a Rabi spectroscopy curve                     is taken. Because both qubits have hybridized one                     will measure two response peaks. This spectrum is                     fit and the splitting between the peaks is related                     to the qubitA-qubit B coupling.                 -   3. Example success criteria can include: (A) The                     fitted chi or qubit-qubit resonance coupling g is                     compared to the design intent.         -   c. Implement gates             -   i. Fixed coupling designs                 -   1. Two qubit Ramsey oscillations                 -    a. For fixed frequency designs the inherent ZZ                     coupling allows a phase accumulation to occur which                     when pre-pended and post pended with single qubit                     gates creates a CNOT-like gate. By performing the                     single qubit gates and varying the time delay the                     gate's action on both qubits can be characterized.                     Further optimization utilizing INEPT pulse sequences                     can be used to enhance the insensitivity to exact                     tuning of the delay time.                 -   2. Example success criteria can include: (A) Delay                     times measured during a Ramsey tune-up are compared                     to calculated wait times, agreement to within a                     specified window denotes success.             -   ii. Tunable qubit designs                 -   1. Fast actuation                 -    a. Similar to the above measurement of 5.c.i.1.a                     the gate is implemented by allowing the two qubits                     to interact for a specified amount of time. However,                     with a tunable qubit one can significantly change                     interaction between qubitA, the tunable qubit, and                     qubit B, the other qubit. A π pulse is first sent to                     qubit A putting it into its excited state.                     Subsequently, a fast DC pulse is sent to the flux                     port of qubit A, this approximately square pulse                     tunes the qubit between a parking flux and an                     interaction flux. By varying the interaction flux                     and the interaction time the states of both qubitA                     and qubit B can be measured. For fixed interaction                     flux set points resonant swapping of which qubit is                     excited in a Rabi flopping manner. The frequency of                     these Rabi Flops can be maximized exactly when the                     interaction flux point brings qubit A into resonance                     with qubit B.                 -   2. Example success criteria can include: (A)                     Successive Rabi flopping curves may need to show                     good fit to the state of each qubit versus the                     interaction time. (B) A maximum swapping Rabi                     frequency must occur. Criteria (A) and (B) may need                     to be both be satisfied.     -   6. Multi qubit benchmarking         -   a. Variations of randomized benchmarking             -   i. Similar to 3.f. a randomized benchmarking can be                 performed which intersperse two qubit swap gates                 throughout a randomized benchmarking sequence.                 Constructing a two qubit randomized benchmarking                 sequence is then a matter of following the excitation                 sequence, but assigning gates to different qubits based                 on the position of the randomized two qubit swaps. By                 bounding how often swaps can occur, an idle qubit can                 have short sequences of single qubit randomized                 benchmarking which returns the idle qubits back to their                 ground state in time to meet their randomly scheduled                 swaps.             -   ii. Example success criteria can include: (A) A decay                 curve is fit to a single qubit gate fidelity number this                 number is compared to a fixed minimum achievable                 fidelity. (B) This experiment is repeated with different                 numbers of two qubit swaps used, the lower fidelity puts                 a bound on the two qubit gate fidelity. Criteria (A)                 and (B) may need to be both be satisfied.         -   b. Optimized gates set tomography             -   i. Similar to 3.g.ii Gate set tomography is taken with a                 reduced gate set.             -   ii. Example success criteria can include: (A) A minimum                 fidelity for each gate may need to be met.

In the following text, additional example experiments are described. Each experiment provides an example of operations to perform all or part of an initialization or calibration process. A central server or other processor can dispatch the processes to sub-processing units or domain control subsystems that operate a domain in a quantum processor cell. In each experiment, the qubits and their measured properties, whose design parameters have been journaled, may be compared and evaluated. The step-by-step process coupled with the computing architecture may allow for the tune-up of large scale superconducting quantum circuit systems.

Some implementations of a two-qubit entangling gate using an alternating fixed-tunable architecture involves adiabatically tuning a flux-tunable transmon such that the two-qubit |1,1> state approaches resonance with the |0,2> state. In this notation, |f,t> indexes the fixed (f) and tunable (t) qubits. Examples of two-qubit entangling gates using a fixed-frequency qubit device and a tunable-frequency qubit device are described in the publication “Parametrically Activated Entangling Gates Using Transmon Qubits” by S. Caldwell, et al., arXiv:1706.06562 [quant-ph], Jun. 20, 2017. In some implementations, an automated process is used for discovering the parameters for such entangling gates. In particular, such parameters can include quantum logic control parameters; as an example, the quantum logic control parameters can include a parameter for a flux pulse configured to implement a controlled-phase (CPHASE) interaction.

In order to find the operating point for a given interaction (for example, a controlled-phase interaction) the follow may need to be determined: (1) the parking point for the tunable qubit, (2) the fast flux pulse amplitude required to throw the qubit to a given interaction location, (3) the fast flux pulse duration that results in a π phase accumulation on the |11> state, and (4) the phases accumulated by the |01> and |10> states during the interaction. The term “zeta” can be referenced herein to refer to the rate of entangling phase accumulation in the CPHASE interaction, e.g., the rate at which the |11> state acquires a phase that may not be acquired by states |01> or |10>. In some cases, a calibration process includes one or more of the following steps performed in the following order or in another order:

-   -   (1) For the determination of the parking point, flux bias         automation can be used to measure the frequency versus flux bias         of the tunable qubit. The bias point can be chosen giving the         tunable parking frequency, such as the maximum or minimum of the         frequency curve.     -   (2) For the determination of the flux pulse amplitude, the         follow can be performed.         -   (a) The zeta versus flux bias data can be taken from flux             bias automation to estimate the desired frequency for the             tunable qubit during the gate.         -   (b) A measurement such as a flux-time Ramsey measurement can             be used to measure the tunable qubit frequency as a function             of flux pulse amplitude.         -   (c) Step (b) can be repeated for several values of amplitude             to sample the frequency versus the amplitude, as shown in             FIG. 5 .         -   (d) This data can be interpolated to identify the amplitude             giving the desired frequency.         -   (e) The desired zeta can be verified by performing a zeta             measurement (for example, by measuring the frequency of the             tunable qubit with the neighbor in both 0 and 1 states, as             the zeta is the difference of the two frequencies). If             necessary, the pulse amplitude can be fine-tuned to obtain             the desired zeta.     -   (3) For the determination of the flux pulse duration, the         following can be performed.         -   (a) The desired phase can be used to estimate the             corresponding gate time using the formula: (desired             phase)=zeta*(duration).         -   (b) For times near the estimated duration, steps 1-3 in FIG.             6 (described below) can be followed.     -   (4) For the |01> and the |10> phases, step 4 in FIG. 6         (described below) can be followed. Accordingly, the information         for the CPHASE can be known for the desired phase angle.

In some implementations, the above technique can be adapted to other physical implementations of CPHASE interactions, beside the use of a flux pulse on a tunable qubit. Such additional implementations can include considerations of how the underlying zeta depends on the implementation. For example, phase tomography, which can be used to find the |01> and |10> phases, can also be extended to another CPHASE gate discovery procedure.

FIG. 5 shows a plot 500 of the qubit frequency in units of megahertz on the y-axis 502 versus the flux pulse amplitude in units of millivolts on the x-axis 504. For the example plot 500, the flux pulse amplitude can range from approximately 320 millivolts to approximately 390 millivolts, and the qubit frequency can range from approximately 3680 megahertz to approximately 3840 megahertz. For the example plot 500, the line 508 characterized by y=2.169*x+2997.631 can be used to fit the points of the plot 500.

FIG. 6 shows a diagram 600 representing example CZ gate tune-up processes 601 and 603. In some implementations, the processes can use phase tomography to obtain phases for qubits. The x-axis can represent phase, and the y-axis can represent amplitude. In particular, process 601 can include a +X/2 phase 602, a +F variable duration τ phase 604, a +X/2 phase 606, and a readout (R0) phase 608. Further, process 603 can include a +X/2 phase 612, a +F variable duration τ phase 614, a +Y/2 phase 616, and a R0 phase 618.

In a first step, phase tomography on fixed transmons can be performed. Accordingly, the phase tomography on fixed transmons can be tunable in the zero state. This can allow for the determination of ϕ₁₀(τ).

In a second step, phase tomography on fixed transmons can be performed. Accordingly, the phase tomography on fixed transmons can be tunable in the one state. This can allow for the determination of ϕ₁₀(τ)+ϕ_(CZ)(τ).

In third step, a subtraction of the phases determined above can be performed. Accordingly, τ* can be determined, where ϕ_(CZ)(τ*)=π. This can allow for the additional determination of ϕ₁₀(τ*), where τ* is the CZ pulse duration.

In a fourth step, phase tomography on tunable transmons can be performed. Accordingly, ϕ₀₁(τ) can be obtained and ϕ₀₁(τ*) can be determined. In some implementations, the CZ gate can thereby be obtained. Thus, the amplitude and duration, ϕ₁₀, ϕ₀₁, and ϕ_(CZ) for the CZ can be thereby obtained.

In some implementations, flux bias automation is used for tunable qubit bring-up. In one implementation, the flux bias automation can include the calibration and characterization of a tunable qubit as a function of a (1) slow (for example, direct current) flux bias, that is, a flux bias voltage or current that is held constant during a set of measurements, or (2) measurements of tunable qubits as a function of fast flux amplitude and fast flux modulation frequency.

In some implementations, flux bias automation (FBA) can refer to a set of measurements that are performed in a specific sequence within a loop over DC flux bias values, with a specific data flow, as shown in FIG. 7 (described in further detail below). In particular, FIG. 7 shows a diagram 700 of a process for flux bias automation. In some implementations, domains can be updated, where the domains can include at least one flux-tunable qubit device; further, sets of measurements can be obtained by performing a measurement sequence within a loop over multiple flux bias values for the flux-tunable qubit device.

In some implementations, when the flux bias is changed, a subset of measurements is performed which can be referred to as repark flux bias and can include (reference to various elements in FIG. 7 are made herein):

-   -   1) Updating the readout point         -   a) A low-power readout can be updated by performing             low-power cavity spectroscopy 716 and updating the readout             frequency to a given point relative to the cavity peaks with             the qubit in the 0 or 1 state.         -   b) A high-power readout can be updated by performing a             cavity power scan at the high-power cavity frequency with             both 0 and 1 qubit preparations, and by determining the             power at which the difference of the two transmission             measurements is maximized.         -   c) The updated readout power or frequency can be saved to             the database 712.     -   2) Updating the qubit frequencies         -   a) Qubit spectroscopy or Ramsey frequency measurement 718             can be performed to obtain the qubit frequency at the new             flux bias.         -   b) The qubit frequency at the new flux bias can be saved to             the database 712.         -   c) The qubit f₀₂/2 can be measured using high-power qubit             spectroscopy.         -   d) The qubit frequency with any neighboring qubits of             interest (for example, for use in two-qubit gates) prepared             in their 1 states can be measured.         -   e) These frequencies or their differences (for example,             qubit-qubit dispersive coupling, e.g., zeta's) from the             frequency found in (a), can be saved to the database,             indexed by the neighbor id.     -   3) Updating the readout optimal quadrature         -   a) A power Rabi measurement 720 can be performed and the             optimal readout quadrature can be identified. In one             implementation, the principal component of the in-phase and             quadrature (IQ) data to find the axis in the IQ plane along             which the sensitivity of the readout to the qubit state is             maximized.) This axis can then be updated.         -   b) The updated optimal quadrature data can be saved to the             database 712.

In some implementations, model and bootstrapping technique for choosing how to automatically construct the qubit frequency measurements is described below. In FBA, the relaxation and coherence times can be measured. With updated readout and gate parameters, the coherence properties of the qubit can be characterized as follows.

-   -   1) T1 can be measured 722 and stored in the database 712.     -   2) T2* can be measured (for example, using Ramsey technique 724)         and can be stored in the database 712.     -   3) T2 echo (for example, including an extra π pulse during a         Ramsey wait) can be measured and stored in the database.     -   4) Step (3) can be repeated for additional n-π pulses. This can         be implemented as a Car-Purcell-Meiboom-Gill (CPMG) experiment.         The decay time for the n π-pulses can be stored in the database         712.

In some implementations, the T2 measurements are constructed such that the fitting returns valid results. In some implementations, this process can provide optimizing gates and performing benchmarking. In some cases, the gates can be optimized, and benchmarking can be performed using one or more of the following steps in the order described or in another order:

-   -   1) An automated 1-qubit gate tune-up can be performed.     -   2) A 1-qubit randomized benchmarking process can be performed.     -   3) A 1-qubit gate set tomography can be performed.         -   a) Other automated fine-tuning and benchmarking processes             can be performed, including, for example, Josephson             parametric amplifier (JPA) optimization.         -   b) Readout point fine-tuning can be performed.

As the DC flux bias of the target is changed, the measured parameters can be stored in a flux dependence table in the database. This can allow for the improvement of interpolation and/or extrapolation, and initial parameter guessing procedures.

-   -   (1) To determine the flux bias value that coarsely corresponds         to one flux quantum, a cavity spectroscopy can be performed as a         function of slow flux bias. This can be used in connection with         the spectrum model for extrapolation, as its flux bias value may         be sensitive to the initial value of flux bias period.     -   (2) After measuring transition frequency f₀₁ (f₁₂) values, the         estimated flux bias period can be used to fit the f₀₁ (f₁₂)         spectrum model. The estimated flux bias period can then be         extrapolated by evaluating the model at the subsequent slow flux         or fast flux value.

In some implementations, additional measurements can be included in the flux bias automation, for example:

-   -   (1) Single-qubit gate optimization at slow flux bias points.     -   (2) Single-qubit randomized benchmarking at slow flux bias         points.

In some implementations, retrying schemes can be implemented for many of the measurements in the flux bias automation, for example:

-   -   (1) Ramsey measurements can determine success criteria based on         the standard error of the mean of the parameters estimated by         one or more fitting models. If the standard error falls outside         of acceptable tolerance ranges, the Ramsey experiment can be         performed again with a larger detuning, smaller span, and         smaller step size.

In addition to measurements as a function of slow flux, tunable qubits can be characterized as a function of fast flux amplitude (with fixed slow flux) and as a function of flux modulation frequency (with fixed slow flux and fast flux amplitude). This allows determination of the following:

-   -   (1) Fast flux pulse throw as a function of flux pulse amplitude.     -   (2) Qubit-qubit dispersive coupling (zetas) as a function of         flux pulse amplitude.     -   (3) Coherence times during fast flux and parametric flux pulse.     -   (4) Modulation detuning as a function of flux pulse amplitude         and frequency.

In addition to fitting the qubit f₀₁ spectrum model, the data collected by these automation procedures can be used to extract other design parameters:

-   -   (1) Resonator frequency vs. slow flux bias.     -   (2) Effective qubit frequency vs fast flux amplitude at fixed         modulation frequency.     -   (3) A direct current crosstalk matrix.     -   (4) A qubit-qubit dispersive coupling (zeta) matrix.     -   (5) A flux noise model.     -   (6) Anharmonicity vs slow flux bias.

For chips with multiple tunable qubits, current on one flux bias line can change the frequencies of other qubits on the same chip, which can be characterized by a DC crosstalk matrix. One or more of the following steps may be performed in the following order or in another order:

-   -   1) A flux-bias point of high sensitivity can be chosen to         incremental flux bias for the tunable qubits.     -   2) The flux bias on the flux bias lines can be incremented. For         each increment the qubit frequency of the (tunable) qubits on         the chip can be measured.     -   3) A two-dimensional matrix (in units of         delta-frequency/delta-flux) can be obtained.     -   4) Using the known frequency curve of each qubit (known from         FBA), this matrix can be converted to units of delta-bias (qubit         1)/delta-bias (qubit 2), which can be dimensionless and constant         across biases.     -   5) This matrix can be stored in a database.

In some implementations, the frequency measurements are bootstrapped, for example, using one or more of the following steps in the following order or in another order:

-   -   1) Starting at zero flux (which can correspond to the maximum         frequency), a small step in positive flux and a small step in         negative flux can be taken. “Small” can mean that the shifted         qubit frequency at the new flux values can still be captured in         the same, or a predictable, frequency span as the qubit         spectroscopy measurement used to capture the qubit frequency at         zero flux.     -   2) These first three frequencies can be fitted to a quadratic         model and the fit can be used to extrapolate the frequencies at         a further point in the positive and negative flux directions.     -   3) Now with five frequency points, the frequencies can be         refitted to a quadratic model and extrapolated again.     -   4) The frequencies can be refitted until there are approximately         ten frequencies. Then the tunable transmon frequency model can         be used to extrapolate and update the tunable transmon         Hamiltonian parameters in the database.     -   5) Some of these steps can be repeated if new frequency         measurements are being obtained.

In some implementations, a Ramsey measurement is built, for example, using one or more of the following operations:

-   -   1) For T2         -   a) Guess what T2 will be (T2_guess).             -   i) Extrapolate from previous trend, for example, by                 using an averaging filter to reduce noise.         -   b) Set the time span from 0 to 4*T2_guess.         -   c) Set the detuning of the reference frame to 1/T2_guess.         -   d) Set the time step to 0.1/T2_guess.     -   2) For frequency         -   a) Guess what the frequency will be.         -   b) Set the time span to an approximately 100 ns window near             zero.         -   c) Set the time step to approximately 1 ns. This can imply a             measurement bandwidth of approximately 100 MHz.         -   d) Set the detuning of the reference frame to approximately             50 MHz away from the guessed frequency.         -   e) This gives sensitivity to frequencies within             approximately 50 MHz of the guessed frequency.

FIG. 7 shows a diagram 700 of a process for flux bias automation. In some implementations, the process includes performing a set of measurements in a particular sequence within a loop over DC flux bias values and with a specific data flow. In particular, diagram 700 includes an analysis 702 process, a resonator spectrum model 704, a f₀₁ spectrum model 706, a f₁₂ spectrum model 708, and a flux noise model 710. Diagram 700 further includes a database 712. Diagram 700 further includes a set flux bias 714 process, cavity frequency spectroscopy 716 process, qubit frequency spectroscopy or Ramsey spectroscopy 718 process, a power Rabi spectroscopy 720 process, a relaxation (T1) 722 process, a Ramsey (T2) 724 process, and an end loop 726 process.

Some processes shown in FIG. 7 include performing a low-power readout from a low-power cavity spectroscopy 716 and updating the readout frequency to a given point relative to cavity peaks associated with the qubit. Additionally, FIG. 7 includes a process of performing a low-power readout from a low-power cavity spectroscopy 716. Moreover, FIG. 7 can further include determining a resonance frequency f_(r), a quality factor (Q_(r)), a readout frequency (f_(ro)), a readout power (P_(ro)), and a coupling parameter χ. The various parameters, including the readout power and the readout frequency can be saved to the database 712.

FIG. 7 includes a process of performing a qubit spectroscopy or Ramsey frequency measurement 718, for example, to obtain the qubit frequency at a given flux bias. Additionally, a frequency f₀₁, a frequency f₀₂/2, the circuit bandwidth (or linewidth) Q_(q), the qubit-qubit dispersive shift ζ and anharmonicity n can be obtained. The various parameters, for example, the qubit frequency at the flux bias can be saved to the database 712.

FIG. 7 further includes a process of performing a power Rabi measurement 720 and identifying the optimal readout quadrature. Additionally, the Rabi oscillation rate Ω can be determined. The updated optimal quadrature data can be saved to the database 712. FIG. 7 additionally shows that T1 can be measured 722 and stored in the database 712. Further, T2* can be measured (using Ramsey technique 724) and stored in the database 712.

In some implementations, the database 712 can be in communication with a processor that can perform or apply one or more of an analysis 702 process, a resonator spectrum model 704, a f₀₁ spectrum model 706, a f₁₂ spectrum model 708, and a flux noise model 710. The database 712 can supply the processor and the models described above with various parameters obtained in processes 714-726.

In some implementations, a calibration process can provide technical advantages for operating a quantum computing system. For instance, the calibration process may provide reliable results by applying well-defined criteria for pass/fail during calibration of superconducting qubits. Design expectations may be used to execute an automated calibration process, providing initial values and the basis of several pass/fail criteria. A calibration routine may be implemented in a manner that is robust to many types of device failure. A computer program with a defined experimental procedure may control the calibration process, which can increase efficiency and consistency while reducing opportunities for error. In some cases, the calibration process can be applied to a very large number of qubits simultaneously, which can enable large-scale quantum computing in some systems. The calibration process may reduce the time used to characterize a device and shorten the design-fabricate-measure cycle.

In some aspects, a computer system controls one or several instruments to generate or measure signals, and an automated calibration process determines one or several control parameters or device characteristics of a specific device under test. The control parameters and device characteristics can be stored in a database. One or more measurement steps can be performed. An experimental procedure can define the order of measurement steps. The experimental procedure can include modular sub-procedures that can be reused or run independently. A measurement step can further include a computerized routine to extract relevant control parameters and device characteristics. A measurement step can further include a computerized routine that determines the “result” of the measurement, where the result includes one or more of: a pointer to the next measurement step in the experimental procedure; a repetition of the current measurement with different parameters; a failure condition which terminates the characterization and calibration cycle; or a success condition which terminates the characterization cycle. Termination in success or failure can trigger a human-readable alert to a configurable set of people. The alert can be sent via email (e.g. SMTP), instant message (e.g. Skype, IRC, Slack), or otherwise. The routine can further include a statistical goodness of fit metric with a defined threshold. The quality of fit metric can include the reduced residual chi-square statistic, the Akaike Information Criterion statistic, the Bayesian Information Criterion statistic or another fit metric. The routine can further include a machine learning algorithm that has been trained, for example, on human-classified measurement results from the same system. The routine can further include one or more statistical goodness of fit metrics with machine learning.

Some of the subject matter and operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Some of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on a computer storage medium for execution by, or to control the operation of, data-processing apparatus. A computer storage medium can be, or can be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them. Moreover, while a computer storage medium is not a propagated signal, a computer storage medium can be a source or destination of computer program instructions encoded in an artificially generated propagated signal. The computer storage medium can also be, or be included in, one or more separate physical components or media (e.g., multiple CDs, disks, or other storage devices).

Some of the operations described in this specification can be implemented as operations performed by a data processing apparatus on data stored on one or more computer-readable storage devices or received from other sources.

The term “data-processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, a system on a chip, or multiple ones, or combinations, of the foregoing. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a cross-platform runtime environment, a virtual machine, or a combination of one or more of them.

A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, object, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

Some of the processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform actions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random-access memory or both. Elements of a computer can include a processor that performs actions in accordance with instructions, and one or more memory devices that store the instructions and data. A computer may also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic disks, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a phone, an electronic appliance, a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive). Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices (e.g., EPROM, EEPROM, flash memory devices, and others), magnetic disks (e.g., internal hard disks, removable disks, and others), magneto optical disks, and CD ROM and DVD-ROM disks. In some cases, the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, operations can be implemented on a computer having a display device (e.g., a monitor, or another type of display device) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse, a trackball, a tablet, a touch sensitive screen, or another type of pointing device) by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user's client device in response to requests received from the web browser.

A computer system may include a single computing device, or multiple computers that operate in proximity or generally remote from each other and typically interact through a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), a network comprising a satellite link, and peer-to-peer networks (e.g., ad hoc peer-to-peer networks). A relationship of client and server may arise by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

In a general aspect, calibration is performed in a quantum computing system.

In a first example, a calibration method includes identifying domains of a quantum computing system by operation of a control system. The domains can include domain control subsystems and subsets of quantum circuit devices in a quantum processor of the quantum computing system. The method can further include obtaining a first set of measurements from a first domain of the domains and storing the first set of measurements in a memory of the control system. The method can include determining, by operation of the control system, device characteristics of the quantum circuit devices of the first domain based on the first set of measurements, and storing the device characteristics in a memory of the control system. The method can further include determining to obtain a second set of measurements from the first domain based on the device characteristics and obtaining the second set of measurements from the first domain. The method can include storing the second set of measurements in the memory of the control system, and determining, by operation of the control system, quantum logic control parameters for the subset of quantum circuit devices of the first domain based on the second set of measurements. The method can further include storing the quantum logic control parameters in a database of the control system for use in operating the first domain.

Implementations of the first example may include one or more of the following features. The domains can be defined in part by hardware, control logic, physical connections, or software in the quantum computing system. The quantum circuit devices of the first domain can include qubit devices and readout devices. The control system can include a controller (where the controller includes a cache), signal conversion circuitry, a filter, and an amplifier. The control system can include an embedded operating system configured to communicate with the database and the controller.

Implementations of the first example may include one or more of the following features. The device characteristics can include resonance frequencies and coherence times for qubit devices in the first domain. The quantum logic control parameters can include read-out pulse parameters or quantum logic gate pulse parameters for qubit devices in the first domain. Further, the method can include repeating the first set of measurements or the second set of measurements based on a success or a failure of a calibration of the first domain of the quantum computing system. The quantum logic control parameters can include a parameter for a flux pulse configured to implement a controlled-phase interaction. The domain can include at least one flux-tunable qubit device. Further, obtaining the first set of measurements can include performing a measurement sequence within a loop over multiple flux bias values for the flux-tunable qubit device.

In a second example, a quantum computing system includes a quantum processor and a control system. The quantum processor includes quantum circuit devices. The control system can be configured to: identify domains of the quantum computing system, the domains comprising respective domain control subsystems and respective subsets of quantum circuit devices. The control system can be further configured to: obtain a first set of measurements from a first domain of the domains; store the first set of measurements in a memory of the control system; determine device characteristics of the quantum circuit devices of the first domain based on the first set of measurements; store the device characteristics in the memory of the control system; and determine to obtain a second set of measurements from the first domain based on the device characteristics. The control system can be configured to: obtain the second set of measurements from the first domain; store the second set of measurements in the memory of the control system; determine quantum logic control parameters for the subset of quantum circuit devices of the first domain based on the second set of measurements; and store the quantum logic control parameters in the database of the control system for use in operating the first domain.

Implementations of the second example may include one or more of the following features. The domains can be defined in part by hardware, control logic, physical connections, or software in the quantum computing system. The quantum circuit devices of the first domain can include qubit devices and readout devices. The control system can include a controller (where the controller includes a cache), signal conversion circuitry, a filter, and an amplifier. The control system can include an embedded operating system configured to communicate with the database and the controller.

Implementations of the second example may include one or more of the following features. The device characteristics can include resonance frequencies and coherence times for qubit devices in the first domain. The quantum logic control parameters can include read-out pulse parameters or quantum logic gate pulse parameters for qubit devices in the first domain. Further, the first set of measurements or the second set of measurements can be repeated based on a success or a failure of a calibration of the first domain of the quantum computing system. The quantum logic control parameters can include a parameter for a flux pulse configured to implement a controlled-phase interaction. The domain can include at least one flux-tunable qubit device. Further, obtaining the first set of measurements can include performing a measurement sequence within a loop over multiple flux bias values for the flux-tunable qubit device.

While this specification contains many details, these should not be understood as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular examples. Certain features that are described in this specification or shown in the drawings in the context of separate implementations can also be combined. Conversely, various features that are described or shown in the context of a single implementation can also be implemented in multiple embodiments separately or in any suitable subcombination.

Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single product or packaged into multiple products.

A number of embodiments have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other embodiments are within the scope of the following claims. 

1-20. (canceled)
 21. A method comprising: identifying, by operation of a control system, domains of a quantum computing system, the domains comprising respective domain control subsystems and respective subsets of quantum circuit devices in a quantum processor of the quantum computing system; performing, by operation of the control system, a first calibration process of a first domain comprising a first subset of quantum circuit devices, wherein performing the first calibration process comprises determining quantum logic control parameters for the first subset of quantum circuit devices; performing, by operation of the control system, a second calibration process of a second domain comprising a second subset of quantum circuit devices, wherein performing the second calibration process comprises determining quantum logic control parameters for the second subset of quantum circuit devices; storing the quantum logic control parameters for the first and second subsets of quantum circuit devices in a database of the control system; using the stored quantum logic control parameters to operate the quantum computing system; and performing, by operation of the control system, a re-calibration process of the first domain.
 22. The method of claim 21, wherein the first calibration process and the second calibration process are performed in parallel.
 23. The method of claim 21, wherein the domains are defined in part by hardware, control logic, physical connections, or software in the quantum computing system.
 24. The method of claim 21, wherein the control system comprises a controller, the controller comprising a cache, signal conversion circuitry, a filter, and an amplifier.
 25. The method of claim 24, wherein the control system comprises an embedded operating system configured to communicate with the database and the controller.
 26. The method of claim 21, comprising performing the re-calibration in response to detecting a drift in the device characteristics of the first subset of quantum circuit devices.
 27. The method of claim 21, wherein the quantum logic control parameters comprise read-out pulse parameters or quantum logic gate pulse parameters.
 28. The method of claim 21, wherein performing the first calibration process comprises: obtaining a first set of measurements from the first domain; determining device characteristics of the quantum circuit devices of the first domain based on the first set of measurements; determining to obtain a second set of measurements from the first domain based on the device characteristics; obtaining the second set of measurements from the first domain; and determining the quantum logic control parameters based on the second set of measurements.
 29. The method of claim 28, wherein performing the re-calibration process of the first domain comprises: repeating the first set of measurements or the second set of measurements to determine updated quantum logic control parameters.
 30. The method of claim 28, comprising performing, by operation of the control system, a re-calibration process of the second domain.
 31. A quantum computing system comprising: a quantum processor comprising quantum circuit devices; and a control system configured to perform operations comprising: identifying domains of the quantum computing system, the domains comprising respective domain control subsystems and respective subsets of the quantum circuit devices in the quantum processor; performing a first calibration process of a first domain comprising a first subset of quantum circuit devices, wherein performing the first calibration process comprises determining quantum logic control parameters for the first subset of quantum circuit devices; performing a second calibration process of a second domain comprising a second subset of quantum circuit devices, wherein performing the second calibration process comprises determining quantum logic control parameters for the second subset of quantum circuit devices; storing the quantum logic control parameters for the first and second subsets of quantum circuit devices in a database of the control system; using the stored quantum logic control parameters to operate the quantum computing system; and performing a re-calibration process of the first domain.
 32. The system of claim 31, wherein the control system is configured to perform the first calibration process and the second calibration process in parallel.
 33. The system of claim 31, wherein the domains are defined in part by hardware, control logic, physical connections, or software in the quantum computing system.
 34. The system of claim 31, wherein the control system comprises a controller, the controller comprising a cache, signal conversion circuitry, a filter, and an amplifier.
 35. The system of claim 31, wherein the control system comprises an embedded operating system configured to communicate with the database and the controller.
 36. The system of claim 31, wherein the operations comprise: performing the re-calibration in response to detecting a drift in the device characteristics of the first subset of quantum circuit devices.
 37. The system of claim 31, wherein the quantum logic control parameters comprise read-out pulse parameters or quantum logic gate pulse parameters.
 38. The system of claim 31, wherein performing the first calibration process comprises: obtaining a first set of measurements from the first domain; determining device characteristics of the quantum circuit devices of the first domain based on the first set of measurements; determining to obtain a second set of measurements from the first domain based on the device characteristics; obtaining the second set of measurements from the first domain; and determining the quantum logic control parameters based on the second set of measurements.
 39. The system of claim 38, wherein performing the re-calibration process of the first domain comprises: repeating the first set of measurements or the second set of measurements to determine updated quantum logic control parameters.
 40. The system of claim 38, wherein the operations comprise: performing a re-calibration process of the second domain. 